Let \(m\) be a positive integer, and let \(a_0, a_1,\ldots,a_m\) be a sequence of integers such that \(a_0 = 37, a_1 = 72, a_m = 0,\) and \(a_{k+1} = a_{k-1} - \frac 3{a_k}\) for \(k = 1,2,\ldots, m-1.\) Find \(m.\)

(第二十三届AIME2 2005 第11题)